A CATEGORICAL INTERPRETATION OF CONTINUOUS ORBIT EQUIVALENCE FOR PARTIAL DYNAMICAL SYSTEMS

Speaker(s)

EUN JI KANG

Affiliation

Seoul National University, South Korea

Language of the talk

English

Date

April 30, 2025, 5:15 p.m.

Information about the event

IMPAN 405 & ZOOM

Title in Polish

A CATEGORICAL INTERPRETATION OF CONTINUOUS ORBIT EQUIVALENCE FOR PARTIAL DYNAMICAL SYSTEMS

Seminar

North Atlantic Noncommutative Geometry Seminar

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We define the orbit morphism of partial dynamical systems, and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a continuous orbit equivalence between the given partial dynamical systems that preserves the essential stabilisers. We show that this is equivalent to the existence of a diagonal-preserving isomorphism between the corresponding crossed products when the essential stabilisers of partial actions are torsion-free and abelian. We also characterize when an étale groupoid is isomorphic to the transformation groupoid of some partial action. Additionally, we explore the implications of this characterization in the context of semi-saturated orthogonal partial dynamical systems over free groups, establishing connections with Deaconu-Renault systems and the concept of eventual conjugacy.

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